Transformations: แบบฝึกหัด

A point with coordinates \((2, 6)\) is reflected in the horizontal line \(y = 3\). Find the coordinates of the reflected image.

Point \(M(-5, 2)\) is reflected in the line \(y = x\). What are the coordinates of the image \(M'\)?

Point \(P(1, 2)\) is mapped onto \(P'(4, 7)\) by an enlargement with a scale factor of \(3\). Find the coordinates of the centre of enlargement.

Point \(P(4, -3)\) is translated by the vector \(\begin{pmatrix} -2 \\ 5 \end{pmatrix}\). What are the coordinates of its image \(P'\)?

Triangle \(T\) has an area of \(15\text{ cm}^2\). It is transformed by an enlargement with a scale factor of \(4\). What is the area of the enlarged image?

A point with coordinates \((5, -2)\) is translated by the vector \(\begin{pmatrix} -3 \\ 4 \end{pmatrix}\). Find the coordinates of the image point.

A vector \(\begin{pmatrix} -4 \\ 2 \end{pmatrix}\) translates point \(P(-1, 6)\). Determine the new coordinates of \(P'\).

Point \(P(4, -1)\) is reflected to point \(P'(-2, -1)\). Determine the equation of the mirror line.

A trapezium T has vertices at \((1, 2)\) , \((3, 2)\) , \((4, 4)\) and \((0, 4)\) .

(a) Enlarge trapezium T by a scale factor of \(0.5\) with the centre of enlargement at the origin \((0, 0)\) to form T'. Write down the coordinates of the vertices of T'.

(b) Calculate the area of trapezium T and the area of trapezium T'. What is the relationship between their areas?

Triangle A has vertices at \((1, 1)\), \((3, 1)\), and \((3, 2)\).

(a) Triangle A is mapped onto Triangle B by a rotation of \(90^\circ\) anticlockwise about the point \((1, 2)\). State the coordinates of the vertices of Triangle B.

(b) Triangle B is then mapped onto Triangle C by an enlargement with scale factor \(-2\) and centre of enlargement at the origin \((0, 0)\). Find the coordinates of the vertices of Triangle C.

(c) Describe fully the single transformation that maps Triangle A onto Triangle D, where Triangle D has vertices at \((2, 2)\), \((6, 2)\), and \((6, 4)\).